QUESTION $2[20$ MARKS$]$

Given a greyscale image as input to a linear classifier with weights and biases as below,

Input $=\left[\begin{array}{cc}37& 75\\ 56& 32\end{array}\right],W=\left[\begin{array}{cccc}-0\mathrm{.}3& -0\mathrm{.}9& 1\mathrm{.}5& 1\mathrm{.}3\\ 1\mathrm{.}7& 2& -0\mathrm{.}7& 0\mathrm{.}1\\ 1\mathrm{.}5& -0\mathrm{.}6& 0& -1\\ 0\mathrm{.}9& 1\mathrm{.}1& -0\mathrm{.}2& 0\mathrm{.}9\end{array}\right],b=\left[\begin{array}{c}17\\ 14\\ 1\\ 3\end{array}\right],$ classes $=\left[\begin{array}{c}\text{e}\text{v}\text{e}\text{r}\text{y}\text{t}\text{h}\text{i}\text{n}\text{g}\\ \text{e}\text{v}\text{e}\text{r}\text{y}\text{w}\text{h}\text{e}\text{r}\text{e}\\ \text{a}\text{l}\text{l}\\ \text{o}\text{n}\text{c}\text{e}\end{array}\right]$

$($a$)$ Calculate the output scores for this input image.

$[4$ Marks$]$

$($b$)$ If $[$everything$]$ is the correct class, calculate the SVM loss.

$[3$ Marks$]$

$($c$)$ If the input image brightness was increased, such that all values are doubled, what

happens to the SVM loss? Simply explain the answer, do NOT perform any

calculations.

$[2$ Marks$]$

$($d$)$ Calculate the cross$-$entropy loss for this input image.

$[3$ Marks$]$

$($e$)$ What are limitations of the linear classifier?

$[3$ Marks$]$

$($f$)$ If the input are colour images of size $225225$ pixels, for $100$ classes, determine the

width, height, and depth of the weight matrix. Provide a brief explanation your answer.

$[2$ marks$]$

$($g$)$ A classification model was trained on the Teachable Machine. Its confusion matrix and

accuracy per class is shown below. Comment on these output results.